Related papers: Fast and Sample Near-Optimal Algorithms for Learni…
The algorithmic tasks of computing the Hamming distance between a given pattern of length $m$ and each location in a text of length $n$ is one of the most fundamental algorithmic tasks in string algorithms. Unfortunately, there is evidence…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
Temporal difference learning and Residual Gradient methods are the most widely used temporal difference based learning algorithms; however, it has been shown that none of their objective functions is optimal w.r.t approximating the true…
In the Maximum Independent Set of Hyperrectangles problem, we are given a set of $n$ (possibly overlapping) $d$-dimensional axis-aligned hyperrectangles, and the goal is to find a subset of non-overlapping hyperrectangles of maximum…
There has been considerable recent interest in distribution-tests whose run-time and sample requirements are sublinear in the domain-size $k$. We study two of the most important tests under the conditional-sampling model where each query…
Clustering is an important technique for identifying structural information in large-scale data analysis, where the underlying dataset may be too large to store. In many applications, recent data can provide more accurate information and…
In this work we solve the problem of robustly learning a high-dimensional Gaussian mixture model with $k$ components from $\epsilon$-corrupted samples up to accuracy $\widetilde{O}(\epsilon)$ in total variation distance for any constant $k$…
Complex design problems are common in the scientific and industrial fields. In practice, objective functions or constraints of these problems often do not have explicit formulas, and can be estimated only at a set of sampling points through…
The primary example of instance-based learning is the $k$-nearest neighbor rule (kNN), praised for its simplicity and the capacity to adapt to new unseen data and toss away old data. The main disadvantages often mentioned are the…
The task of extracting a diverse subset from a dataset, often referred to as maximum diversification, plays a pivotal role in various real-world applications that have far-reaching consequences. In this work, we delve into the realm of…
Reinforcement learning (RL) algorithms based on high-dimensional function approximation have achieved tremendous empirical success in large-scale problems with an enormous number of states. However, most analysis of such algorithms gives…
Optimal decision tree (\odt) is a fundamental problem arising in applications such as active learning, entity identification, and medical diagnosis. An instance of \odt is given by $m$ hypotheses, out of which an unknown ``true'' hypothesis…
From a fresh data science perspective, this thesis discusses the prediction of coronary artery disease based on genetic variations at the DNA base pair level, called Single-Nucleotide Polymorphisms (SNPs), collected from the Ontario Heart…
We present the first mathematical analysis of stochastic density functional theory (DFT) in the context of the Hartree approximation. We motivate our analysis via the notion of nearly-optimal or $\tilde{O}(n)$ scaling with respect to the…
A decision tree recursively splits a feature space $\mathbb{R}^{d}$ and then assigns class labels based on the resulting partition. Decision trees have been part of the basic machine-learning toolkit for decades. A large body of work treats…
A very simple example of an algorithmic problem solvable by dynamic programming is to maximize, over sets A in {1,2,...,n}, the objective function |A| - \sum_i \xi_i 1(i \in A,i+1 \in A) for given \xi_i > 0. This problem, with random…
We study representation learning for efficient imitation learning over linear systems. In particular, we consider a setting where learning is split into two phases: (a) a pre-training step where a shared $k$-dimensional representation is…
Dimensionality reduction (DR) algorithms, which reduce the dimensionality of a given data set while preserving the information of the original data set as well as possible, play an important role in machine learning and data mining. Duan…
The $K$-nearest neighbors is a basic problem in machine learning with numerous applications. In this problem, given a (training) set of $n$ data points with labels and a query point $p$, we want to assign a label to $p$ based on the labels…
Multi-index models - functions which only depend on the covariates through a non-linear transformation of their projection on a subspace - are a useful benchmark for investigating feature learning with neural nets. This paper examines the…